# Work and Kinetic Energy: Calculating Work and Speed with Varying Force

• shenwei1988
In this case, the force is changing with respect to displacement, so you cannot just use the formula F*d. Instead, you need to integrate the force equation from the initial position (x = 0) to the final position (x = 2.78). This will give you the total work done by the force on the mass.In summary, the magnitude of a one-dimensional force is given by the equation F = 6.68x^2 + 1.56, where x is the displacement from the origin and F is the force in Newtons. At t = 0, a 677 g mass is at the origin moving in the positive x-direction at a speed of 8.46 m/s when this force
shenwei1988
The magnitude of a certain one-dimensional force varies according to:

F = 6.68x^2 + 1.56

where x is the displacement from the origin in meters, and F is the force in Newtons. At t = 0, a 677 g mass is at the origin moving in the positive x-direction at speed 8.46 m/s when this force begins to act on it.
ASSUME: there are no other forces acting on the mass.

a) How much work is done by the force on the mass when it reaches x = 2.78 m?
b) What is the speed of the mass when it reaches 2.78 m?

W=FS

i put x=2.78 into the equation. w=(6.68*2.78^2)*2.78

## The Attempt at a Solution

shenwei1988 said:
i put x=2.78 into the equation. w=(6.68*2.78^2)*2.78

If you put the value of x, you get the force, not the work. Think about what is work done in terms of force and distance.

not, i put the value of x. and get the force, then use the force * distance.w=(6.68*2.78^2+1.56)*2.78

When the force is not constant, then the work done is Integral(from x1 to x2)[Fdx].

## 1. What is work?

Work is the measure of force applied over a distance. It is calculated by multiplying the force applied by the distance traveled in the direction of the force.

## 2. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is calculated by multiplying half of the object's mass by its velocity squared.

## 3. How are work and kinetic energy related?

Work and kinetic energy are directly related. The work done on an object is equal to the change in kinetic energy of that object.

## 4. Can work be negative?

Yes, work can be negative. This occurs when the force and displacement are in opposite directions, resulting in a decrease in kinetic energy.

## 5. How is the unit of work and kinetic energy measured?

The unit of work and kinetic energy is measured in joules (J) in the International System of Units (SI).

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